Plane Strain Research Articles

Seismic Response of Tunnels Under Effect of Overburden Depth Using Simplified Pseudo-Static Analysis

Earthquakes are one of the natural occurrences that can lead to massive disasters, either on structures or infrastructure. The seismic response and performance of underground infrastructure such as tunnels against earthquake vibrations is predictably severe due to the complex interaction between tunnels and the surrounding soil, especially one embedded in poor soil material properties. In view of this, previous experiences of tunnel damages subjected to earthquake loads have been reported in the literature. Thus, rigorous analysis is necessary to provide indepth knowledge and understanding of the seismic response of tunnels which beneficial to engineering practitioners in especially in early design stage in order to avoid the future risk of tunnel damage and failure during an unpredictable earthquake event. The aim of this study is to investigate the effect of overburden depth on seismic response of tunnels using the simplified pseudo-static analysis, while simultaneously to emphasize the shortcoming of conventional closed-form solution. This study presents a two-dimensional (2D) simplified pseudo-static analysis of soil-tunnel model embeded at 10m and 20m overburden depth subjected to increasing levels of seismic intensity at the transverse direction of tunnel axis. The numerical investigation was performed using the finite element program PLAXIS 2D. The circular shaped tunnel lining are assumed to be elastic, while the soil is considered as homogeneous, and isotropic in plane strain condition. Considering the complex soil-tunnel interaction, the tunnel lining and soil interface is assumed as no-slip condition. The numerical result of pseudo-static analyses were compared with the conventional closed-form Wang‘s analytical solution to verify the reliability of the obtained results. The results denoted that the tunnel embedded at 10m overburden depth experienced considerable seismic-induced deformation and structural forces than tunnel buried at 20m depth. The deformation and seismic induced structural forces of tunnel increased with increment on the magnitude of earthquake loadings. Thus, it can be concluded that the shallow tunnel suffered more damages compared to the tunnel embedded at deeper depth. Overburden depth of tunnel plays a significant role in modifying the seismic response of tunnel apart of the imposed magnitude of earthquake loadings. The conventional closed-form analytical method tends to overestimate the seismic response of tunnel compared to numerical pseudo-static analysis.

The Port-Hamiltonian Structure of Continuum Mechanics

In this paper, we present a novel approach to the geometric formulation of solid and fluid mechanics within the port-Hamiltonian framework, which extends the standard Hamiltonian formulation to non-conservative and open dynamical systems. Leveraging Dirac structures, instead of symplectic or Poisson structures, this formalism allows the incorporation of energy exchange within the spatial domain or through its boundary, which allows for a more comprehensive description of continuum mechanics. Building upon our recent work in describing nonlinear elasticity using exterior calculus and bundle-valued differential forms, this paper focuses on the systematic derivation of port-Hamiltonian models for solid and fluid mechanics in the material, spatial, and convective representations using Hamiltonian reduction theory. This paper also discusses constitutive relations for stress within this framework including hyper-elasticity, for both finite and infinitesimal strains, as well as viscous fluid flow governed by the Navier–Stokes equations.

Homogenization using lattice spring models for couple stress theory under plane strain deformation

Homogenization using lattice spring models for couple stress theory under plane strain deformation

A Force-Sensor-Less Approach for Rapid Young's Modulus Identification of Heterogeneous Soft Tissue.

Due to individual differences, accurate identification of tissue elastic parameters is essential for biomechanical modeling in surgical guidance for hepatic venous injections. This paper aims to acquire the absolute Young's modulus of heterogeneous soft tissues during endoscopic surgery with 2D ultrasound images. First, we introduced a force-sensor-less approach that utilizes a pre-calibrated soft patch with a known Young's modulus and its ultrasound images to calculate the external forces exerted by the probe on the tissue. Second, we introduced a Kriging-based inverse algorithm to identify the relative Young's modulus (RYM) between the inclusion and the background tissue. The RYM was estimated based on 2D plane strain approximation and mapped to the RYM of 3D soft tissue through a trained Kriging model. Finally, we developed a direct method to identify the background Young's modulus (BYM) based on calculated external forces and RYM. The simulation results demonstrate the high efficiency and robustness of the Kriging-based inverse algorithm in identifying RYM. Physical experiments on the three phantoms show that the errors of the identified BYM and RYM are all below 15%. The proposed methodology for Young's modulus identification is feasible and achieves satisfactory accuracy and computational efficiency in both simulations and physical experiments.

Towards higher electro-optic response in AlScN

Novel materials with large electro-optic (EO) coefficients are essential for developing ultra-compact broadband modulators and enabling effective quantum transduction. Compared to lithium niobate, the most widely used nonlinear optical material, wurtzite AlScN, offers advantages in nano-photonic devices due to its compatibility with integrated circuits. We perform detailed first-principles calculations to investigate the electro-optic effect in Al1−xScxN alloys and superlattices. At elevated Sc concentrations in alloys, the EO coefficients increase; importantly, we find that cation ordering along the c axis leads to enhanced EO response. Strain engineering can be used to further manipulate the EO coefficients of AlScN films. With applied in-plane strains, the piezoelectric contributions to the EO coefficients increase dramatically, even exceeding 250 pm/V. We also explore the possibility of EO enhancement through superlattice engineering, finding that nonpolar a-plane (AlN)m/(ScN)n superlattices increase EO coefficients beyond 40 pm/V. Our findings provide design principles to enhance the electro-optic effect through alloy engineering and heterostructure architecture.

Engineering Nonvolatile Polarization in 2D α-In2Se3/α-Ga2Se3 Ferroelectric Junctions

The advent of two-dimensional (2D) ferroelectrics offers a new paradigm for device miniaturization and multifunctionality. Recently, 2D α-In2Se3 and related III–VI compound ferroelectrics manifest room-temperature ferroelectricity and exhibit reversible spontaneous polarization even at the monolayer limit. Here, we employ first-principles calculations to investigate group-III selenide van der Waals (vdW) heterojunctions built up by 2D α-In2Se3 and α-Ga2Se3 ferroelectric (FE) semiconductors, including structural stability, electrostatic potential, interfacial charge transfer, and electronic band structures. When the FE polarization directions of α-In2Se3 and α-Ga2Se3 are parallel, both the α-In2Se3/α-Ga2Se3 P↑↑ (UU) and α-In2Se3/α-Ga2Se3 P↓↓ (NN) configurations possess strong built-in electric fields and hence induce electron–hole separation, resulting in carrier depletion at the α-In2Se3/α-Ga2Se3 heterointerfaces. Conversely, when they are antiparallel, the α-In2Se3/α-Ga2Se3 P↓↑ (NU) and α-In2Se3/α-Ga2Se3 P↑↓ (UN) configurations demonstrate the switchable electron and hole accumulation at the 2D ferroelectric interfaces, respectively. The nonvolatile characteristic of ferroelectric polarization presents an innovative approach to achieving tunable n-type and p-type conductive channels for ferroelectric field-effect transistors (FeFETs). In addition, in-plane biaxial strain modulation has successfully modulated the band alignments of the α-In2Se3/α-Ga2Se3 ferroelectric heterostructures, inducing a type III–II–III transition in UU and NN, and a type I–II–I transition in UN and NU, respectively. Our findings highlight the great potential of 2D group-III selenides and ferroelectric vdW heterostructures to harness nonvolatile spontaneous polarization for next-generation electronics, nonvolatile optoelectronic memories, sensors, and neuromorphic computing.

Decoding the Hume-Rothery Rule in a Bifunctional Tetra-metallic Alloy for Alkaline Water Electrolysis.

The 90-year-old Hume-Rothery rule was adapted to design an outstanding bifunctional tetra-metallic alloy electrocatalyst for water electrolysis. Following the radius mismatch principles, Fe (131 pm) and Ni (124 pm) are selectively incorporated at the Pd (139 pm) site of Mo0.30Pd0.70 nanosheets. Analogously, Cu (132 pm) alloys with only Pd, while Ag (145 pm) alloys with both Pd and Mo (154 pm). The face-centered cubic Mo0.30Pd0.35Ni0.23Fe0.12 nanosheets with 10-12 atomic layers, featuring in-plane compressive strain along the {111} basal plane, show 1/3 (422) reflection from local hexagonal symmetry. The more electronegative Pd attracts electron density from Ni/Fe in Mo0.30Pd0.35Ni0.23Fe0.12, synergistically boosting the mass activities for hydrogen and oxygen evolution reactions to 89 ± 5 and 38.6 ± 3.1 A g-1 at ±400 mV versus RHE, respectively. Full water electrolysis continues for ≥550 h, requiring cell voltages of 1.51 and 1.63 V at 10 and 100 mA cm-2, delivering 45 mL h-1 green H2.

Low-Frequency Longitudinal Vibrations of a Fluid-Loaded Elastic Layer

This paper concerns the low-frequency symmetric (extensional) motions of a thin elastic layer submerged in a fluid. This problem is less investigated than that for antisymmetric motion corresponding to bending vibrations, partly because the classical theory for thin-plate extension is not oriented to model the transverse compression of the plate caused by the pressure of the fluid. It is also worth noting that, in contrast to a fluid-borne bending wave, the extensional wave radiates into the fluid, resulting in complex-valued terms in the associated dispersion relation. In this paper, we derive a refined asymptotic formulation for symmetric motion starting from the 2D plane strain problem regarding fluid–structure interaction. The obtained results have the potential to be implemented for interpreting numerical and experimental data for a variety of modern engineering setups.

Strain manipulation of spin-polarized topological phase in WSe2/CrI3 heterostructure

Here, based on first-principles calculations and topological analysis, we show that the spin-polarized topological phase is present in a van der Waals (vdW) heterostructure WSe2/CrI3. We reveal that magnetism induced by proximity effects in the heterostructure breaks the time-reversal symmetry (TRS) and thus induces gapped topological edge states, exhibiting the TRS-breaking quantum spin Hall (QSH) effect. By applying a stress field, the WSe2/CrI3 heterostructure manifests enhanced spin polarization, Rashba splitting, and tunable bandgap. The TRS-breaking QSH effect observed in the WSe2/CrI3 heterostructure exhibits remarkable robustness against interlayer shearing. The distinct anisotropy associated with in-plane strain provides precise manipulation strategies for bandgap engineering. Notably, in-plane tensile strain can significantly increase the nontrivial bandgap by up to 98 meV, suggesting the magnetic WSe2/CrI3 heterostructure represents an outstanding platform for achieving the TRS-breaking QSH effect at room temperature. Our findings provide a theoretical foundation for the development of low-dissipation spintronic nanodevices.

Uniform elastic field within a parabolic inhomogeneity obeying Neuber’s nonlinear stress-strain law under generalized plane strain deformations

We use complex variable methods to derive a closed-form solution to the generalized plane strain problem of an incompressible nonlinear elastic parabolic inhomogeneity obeying Neuber’s special nonlinear stress-strain law embedded in an infinite linear isotropic elastic matrix subjected to uniform remote in-plane and anti-plane stresses. We prove that the internal in-plane and anti-plane stresses and strains within the parabolic inhomogeneity remain uniform. The uniform effective strain within the parabolic inhomogeneity is obtained in closed-form. Consequently, the uniform elastic field within the parabolic inhomogeneity and the non-uniform elastic field in the matrix are completely determined.

Application of Surface-Cracking Process to Improve Impact Toughness of High-Strength BCC Steel at Low Temperatures

At very low temperatures, typically ductile materials, especially body-centered cubic (BCC) steels, often exhibit an abrupt transition to brittle fracture, significantly limiting their applicability in cryogenic and low-temperature environments. This challenge arises from the inherent properties of BCC steels, where ductility is drastically reduced, leading to unexpected failures under mechanical stress. Despite the advantages of high-strength BCC steels, including cost-effectiveness and mechanical robustness, their susceptibility to brittle fracture restricts their use in demanding low-temperature applications. To address this limitation, we developed an innovative surface-cracking process to enhance the impact toughness of BCC steels. The introduction of controlled surface cracks redistributes stress and energy dissipation mechanisms, improving the toughness of high-strength BCC steels at cryogenic temperatures. Microscopic observations and finite element analyses reveal that these surface cracks not only dissipate crack formation energy but also alter stress triaxiality at crack tips. This causes the stress state to transition toward a plane stress condition, effectively mitigating stress concentrations typically observed in plane strain states. By reducing localized stress severity and promoting uniform energy distribution, the surface cracks encourage failure mechanisms favoring ductile behavior over brittle fracture.

Theoretical understanding of the in-plane tensile strain effects on enhancing the ferroelectric performance of Hf0.5Zr0.5O2 and ZrO2 thin films.

In-plane tensile strain was reported to enhance the ferroelectricity of Hf1-xZrxO2 thin films by promoting the formation of a polar orthorhombic (PO-) phase. However, its origin remains yet to be identified unambiguously, although a strain-related thermodynamic stability variation was reported. This work explores the kinetic effects that have been overlooked to provide a precise answer to the problem, supplementing the thermodynamic calculations. The in-plane strain-dependent phase fractions were identified by calculating the relative influences of the thermodynamic factor (Boltzmann distribution of free energies of polymorphs) and the kinetic factor (transition rate between polymorphs using the Johnson-Mehl-Avrami equation). The monoclinic (M-) phase constitutes the ground state under almost all conditions. However, its formation is kinetically suppressed by the high activation barrier for the transition from the tetragonal (T-) phase. In contrast, PO-phase formation is dominated by thermodynamic effects and is promoted under in-plane tensile strain due to the energetic stabilization of the PO-phase, while the T- to PO-phase transition is kinetically probable due to a low activation barrier. The in-plane tensile strain also lowers the activation barrier of T → M. Hence, the optimal tensile strain for PO-phase formation varies depending on the thermal conditions. The remanent polarization was calculated using spontaneous polarization and the PO-phase fraction. The in-plane tensile strain of 2-2.5% and moderate annealing at approximately 700 K were optimum for increasing ferroelectricity by 34% in Hf0.5Zr0.5O2 and 106% in ZrO2 along the 〈111〉 orientation.

Strain-engineered bright excitons and a nearly flat band in monolayer SnNBr for high-speed LED applications.

With the ever-increasing volume of data, the need for systems that can handle massive datasets is becoming gradually critical. High performance visible light communication (VLC) systems offer an expedient solution, yet its widespread adoption is hindered by the limited modulation bandwidth of light emitting diodes (LEDs). Through ab initio many-body perturbation theory within the GW approximation and the Bethe-Salpeter equation (BSE) approach, this work introduces a novel approach to achieving exceptionally high modulation bandwidth by utilizing the nearly flat bands in two-dimensional semiconductors, using SnNBr monolayer as a prototype material for overcoming this bottleneck. Utilizing its unique properties of a direct bandgap and a nearly flat highest valence band, we demonstrate the achievement of exceptionally high modulation bandwidths on the order of terahertz, surpassing the capabilities of established materials such as InGaN and GaN. Interestingly, the excellent absorption and recombination features of the SnNBr monolayer can be modulated further by the application of in-plane tensile strain. The strain-induced proliferation of bright excitons in the visible region, coupled with enhanced absorption and accelerated recombination rates, provides a deeper understanding of the fundamental mechanisms at play in two-dimensional materials, laying the groundwork for future explorations in light-matter interactions at terahertz frequencies.

Estimating in vivo power deposition density in thermotherapies based on ultrasound thermal strain imaging.

In thermal therapies, accurate estimation of in-tissue power deposition density (PDD) is essential for predicting temperature distributions over time or regularizing temperature imaging. Based on our previous work on ultrasound thermometry, namely, multi-thread thermal strain imaging (MT-TSI), this work develops an in vivo PDD estimation method. Specifically, by combining the TSI model infinitesimal echo strain filter with the bio-heat transfer theory (the Pennes equation), a finite-difference time-domain model is established to allow online extraction of the PDD. An alternating-direction implicit method is adopted to ensure numerical stability and computational efficiency in implementing the model. Based on simulations, the accuracy and effectiveness of the model are examined by comparing a preset PDD distribution with the estimated one. Then, TSI results are obtained from ultrasound data acquired in in vivo experiments; with the PDD estimated from that, TSI distributions are then "predicted" using a validated numerical procedure. The two TSI results are compared to verify the self-consistency of the proposed method. A simplified and more efficient protocol for obtaining an "equivalent spherical PDD" is also discussed.

Plane strain problems for flexoelectric semiconductors

Plane strain problems for flexoelectric semiconductors

Mechanisms of slip modes and texture inheritance in Ti60 alloy during plane strain compression: Insights from texture evolution and regulation

Mechanisms of slip modes and texture inheritance in Ti60 alloy during plane strain compression: Insights from texture evolution and regulation

Yet another best approximation isotropic elasticity tensor in plane strain

Yet another best approximation isotropic elasticity tensor in plane strain

The Influence of the Strain Rate on Texture Formation During the Plane Strain Compression of AZ80 Magnesium Alloy.

Controlling microstructure and texture development is a key approach to improving the formability of magnesium alloys. In this study, the effects of the strain rate and initial texture on the texture evolution of magnesium alloys during high-temperature processing are investigated. The plane strain compression of three types of AZ80 magnesium alloys with different initial textures was assessed at 723 K and a train rate of 0.0005 s-1. Work softening was consistently observed in the stress-strain curves of all samples. However, the peak stress varied depending on the initial texture, with lower peak stress observed under conditions favoring prismatic slip. Under these conditions, the activation of non-basal slip suppressed the formation of basal texture. The texture shifted and developed parallel to the transverse direction when prismatic slip was dominant. In contrast, the activation of pyramidal slip led to the formation of a basal texture tilted by 25° from the (0001) plane. The effects of recrystallization and grain boundary migration on texture development were minimal. This study contributes to understanding the texture development mechanisms in magnesium alloys and provides insights into improving their workability and ductility through texture modification.

Crystal Plasticity Finite Element Study on Orientation Evolution and Deformation Inhomogeneity of Island Grain During the Ultra-Thin Strips Rolling of Grain Oriented Electrical Steel.

The presence of island grains in the initial finished sheets of grain-oriented electrical steel is inevitable in the preparation of ultra-thin strips. Owing to their distinctive shape and size effects, their deformation behavior during rolling differs from that of grain-oriented electrical steels of conventional thickness. This study focuses on the orientation evolution and deformation heterogeneity of island grains during rolling. Four types of island grains with orientations of {210}<001>, {110}<112>, {114}<481>, and {100}<021> were selected and modeled within the Goss-oriented matrix using full-field crystal plasticity finite element (CPFEM) simulation under plane strain compression. The results are then compared with corresponding experimental measurements. The results reveal that orientation rotation and grain fragmentation vary among the island grains of different orientations, with the first two orientations exhibiting more significant deformation heterogeneity compared to the latter two. Additionally, the orientations of the island grains significantly affect the distribution of residual Goss orientations within the surrounding matrix. Pancake-like island grains exhibit a higher degree of orientation scatter and greater deformation heterogeneity in the central layer compared to their spherical counterparts. The initial {210}<001> island grains can form a cube orientation, which can be optimized by subsequent process control to enhance magnetic properties.

Hypersensitive meta-crack strain sensor for real-time biomedical monitoring.

Real-time monitoring of infinitesimal deformations on complex morphologies is essential for precision biomechanical engineering. While flexible strain sensors facilitate real-time monitoring with shape-adaptive properties, their sensitivity is generally lower than spectroscopic imaging methods. Crack-based strain sensors achieve enhanced sensitivity with gauge factors (GFs) exceeding 30,000; however, such GFs are only attainable at large strains exceeding several percent and decline below 10 for strains under 10-3, rendering them inadequate for minute deformations. Here, we introduce hypersensitive and flexible "meta-crack" sensors detecting infinitesimal strains through previously undiscovered crack-opening mechanisms. These sensors achieve remarkable GFs surpassing 1000 at strains of 10-4 on substrates with a Poisson's ratio of -0.9. The crack orientation-independent gap-widening behavior elucidates the origin of hypersensitivity, corroborated by simplified models and finite element analysis. Additionally, parallel mechanical circuits of meta-cracks effectively address the trade-off between resolution and maximum sensing threshold. In vivo real-time monitoring of cerebrovascular dynamics with a strain resolution of 10-5 underscores the hypersensitivity and conformal adaptability of sensors.